| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
We found several new aspects of the solutions and mathematical structures for ultradiscrete (both of the independent and dependent variables are discrete), and related discrete equations. We also studied the relationship between the solutions of ultradiscrete equations and those of the corresponding nonlinear differential equations, and made clear that both are closely related. We also proposed a Kalman filter for the ultradiscrete system corresponding to a nonlinear difference equation and confirmed its validity through numerical experiment. This result strongly suggests an applicability of the ultradiscrete equations to engineering systems. Furthermore, we propose a new type of nonlocal nonlinear difference equation, which is a model of traffic flow and can give a new insight on the relation between discrete and ultradiscrete systems.
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